The Levi Problem On Strongly Pseudoconvex $G$-Bundles

Details The Levi Problem On Strongly Pseudoconvex $G$-Bundles The Levi Problem On Strongly Pseudoconvex $G$-Bundles

2008-02-27

arxiv.org/abs/0802.3981v5

Ann. Glob. Anal. Geom. (2010), v.37, 1--20

Mathematics

Complex Variables

19 pages--Corrects earlier versions

Scientific paper

10.1007/s10455-009-9170-z

Let $G$ be a unimodular Lie group, $X$ a compact manifold with boundary, and
$M$ the total space of a principal bundle $G\to M\to X$ so that $M$ is also a
strongly pseudoconvex complex manifold. In this work, we show that if $G$ acts
by holomorphic transformations satisfying a local property, then the space of
square-integrable holomorphic functions on $M$ is infinite $G$-dimensional.

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